Room 202, Astronomy-Mathematics Building, NTU

(台灣大學天文數學館 202室)

On Common Divisors of Elliptic Sequences over Function Fields

Liang-Chung Hsia (
National Taiwan Normal University
)

Abstract

In this talk, we'll discuss the common divisors among sequences arising from cyclic groups generated by rational points of elliptic curves () defined over the function field of a smooth projective curve over . More precisely, let be the elliptic surfaces over with generic fiber and let be sections (corresponding to points of the generic fibers) of (for ). The question that we're concerned with is whether or not there are infinitely many such that for some integers we have on (for ). We provide an answer to this question. A special case of our result answers a conjecture made by Silverman.

This is a joint work with Dragos Ghioca and Tom Tucker.